Hi, I am following a course of Mathematics, I got a problem as my home work as follows; Please give me a help to fing out the answer for following RLC problem. An R.L.C. circuit has an emf of 100 cos2t, a resistance of 80Ω, an inductance of 20H and capacitance of 10^-2 F. Find an expression for the charge at any time t.
Hi thanks for the reply, actually this my home work is include in the Fourier series class, if there any other path is available for answer this qustion please let me know (differentiating or ..). The question is not directly print as these are in series. but normally these are in series.
OK, if they are in series, then you should be able to find an expression like this :- Voltage source = Voltage across resistor + voltage across capacitor + voltage across inductor Try to express this in terms of charge at any time t. Yes, you can use calculus.
The RLC circuit is characterised by a second order differential equation. If you manage to get the differential equation right, and IF the condition of inital rest applies (y = 0 for x<0, meaning it is a linear time invariant system, and since it's BIBO stable (bounded input bounded output)) the laplace transform will converge on the jω axis meaning that the fourier transform does exist.... then you can apply the fourier transform on the differential equation and solve it. If it has nonzero inital conditions you need to use the laplace transformation. But since you're in a fourier course then i assume the conditions above apply.